Practical limitations of quantum data propagation on noisy quantum processors

TL;DR

This paper investigates the impact of noise on quantum data propagation in variational quantum algorithms, showing that low-error gates are essential for reliable results on current noisy quantum processors.

Contribution

It provides quantitative bounds on how noise affects variational parameter propagation and highlights the necessity of very low error rates for reliable quantum computations.

Findings

Error in variational parameters scales with noise probability

Exact error expressions derived for depolarizing noise

Reliable quantum data propagation requires extremely low error gates

Abstract

The variational quantum imaginary time evolution algorithm is efficient in finding the ground state of a quantum Hamiltonian. This algorithm involves solving a system of linear equations in a classical computer and the solution is then used to propagate a quantum wavefunction. Here, we show that owing to the noisy nature of current quantum processors, such a quantum algorithm or the family of quantum algorithms will require single- and two-qubit gates with very low error probability to produce reliable results. Failure to meet such condition will result in erroneous quantum data propagation even for a relatively small quantum circuit ansatz. Specifically, we provide the upper bounds on how the relative error in variational parameters' propagation scales with the probability of noise in quantum hardware. We also present an exact expression of how the relative error in variational parameter propagation scales with the probability of partially depolarizing noise.